Presentation is loading. Please wait.

Presentation is loading. Please wait.

Statistical Description of Multipath Fading

Similar presentations


Presentation on theme: "Statistical Description of Multipath Fading"— Presentation transcript:

0 Properties of the Mobile Radio Propagation Channel
Jean-Paul M.G. Linnartz Nat.Lab., Philips Research

1 Statistical Description of Multipath Fading
Mobile Radio Propagation Channel Statistical Description of Multipath Fading The basic Rayleigh / Ricean model gives the PDF of envelope But: how fast does the signal fade? How wide in bandwidth are fades? Typical system engineering questions: What is an appropriate packet duration, to avoid fades? How much ISI will occur? For frequency diversity, how far should one separate carriers? How far should one separate antennas for diversity? What is good a interleaving depth? What bit rates work well? Why can't I connect an ordinary modem to a cellular phone? The models discussed in the following sheets will provide insight in these issues Multipath fading

2 The Mobile Radio Propagation Channel
A wireless channel exhibits severe fluctuations for small displacements of the antenna or small carrier frequency offsets. Amplitude Frequency Time Channel Amplitude in dB versus location (= time*velocity) and frequency Multipath fading

3 Some buzz words about Time Dispersion and Frequency Dispersion
Mobile Radio Propagation Channel Some buzz words about Time Dispersion and Frequency Dispersion Time Dispersion Frequency Dispersion Time Domain Channel variations Delay spread Interpretation Fast Fading InterSymbol Interference Correlation Distance Channel equalization Frequency Doppler spectrum Frequency selective fading Domain Intercarrier Interference Coherence bandwidth Interpretation Multipath fading

4 Fading is characterised by two distinct mechanisms
Mobile Radio Propagation Channel Fading is characterised by two distinct mechanisms 1. Time dispersion Time variations of the channel are caused by motion of the antenna Channel changes every half a wavelength Moving antenna gives Doppler spread Fast fading requires short packet durations, thus high bit rates Time dispersion poses requirements on synchronization and rate of convergence of channel estimation Interleaving may help to avoid burst errors 2. Frequency dispersion Delayed reflections cause intersymbol interference Channel Equalization may be needed. Frequency selective fading Multipath delay spreads require long symbol times Frequency diversity or spread spectrum may help Multipath fading

5 Time dispersion of narrowband signal (single frequency)
Mobile Radio Propagation Channel Time dispersion of narrowband signal (single frequency) Transmit: cos(2p fc t) Receive: I(t) cos(2p fc t) + Q(t) sin(2p fc t) = R(t) cos(2p fc t + f) I-Q phase trajectory As a function of time, I(t) and Q(t) follow a random trajectory through the complex plane Intuitive conclusion: Deep amplitude fades coincide with large phase rotations Multipath fading

6 Mobile Radio Propagation Channel
Doppler shift All reflected waves arrive from a different angle All waves have a different Doppler shift The Doppler shift of a particular wave is Maximum Doppler shift: fD = fc v / c Joint Signal Model Infinite number of waves Uniform distribution of angle of arrival f: fF(f) = 1/2p First find distribution of angle of arrival the compute distribution of Doppler shifts Line spectrum goes into continuous spectrum Doppler

7 Mobile Radio Propagation Channel
Doppler Spectrum If one transmits a sinusoid, … what are the frequency components in the received signal? Power density spectrum versus received frequency Probability density of Doppler shift versus received frequency The Doppler spectrum has a characteristic U-shape. Note the similarity with sampling a randomly-phased sinusoid No components fall outside interval [fc- fD, fc+ fD] Components of + fD or -fD appear relatively often Fades are not entirely “memory-less” Doppler

8 Autocorrelation of the signal
Mobile Radio Propagation Channel Autocorrelation of the signal We now know the Doppler spectrum. But how fast does the channel change? Wiener-Kinchine Theorem: Power density spectrum of a random signal is the Fourier Transform of its autocorrelation Inverse Fourier Transform of Doppler spectrum gives autocorrelation of I(t) and Q(t) Autocorrelation

9 Autocovariance of amplitude
Mobile Radio Propagation Channel Autocovariance of amplitude ( ) C J 2 f D = p t Autocorrelation

10 How to handle fast multipath fading?
Mobile Radio Propagation Channel How to handle fast multipath fading? Multipath fading

11 Frequency Dispersion Frequency dispersion is caused by the delay spread of the channel Frequency dispersion has no relation to the velocity of the antenna Multipath fading

12 Frequency Dispersion: Delay Profile
Mobile Radio Propagation Channel Frequency Dispersion: Delay Profile Multipath fading

13 Mobile Radio Propagation Channel
Typical Delay Spreads Multipath fading

14 Channel Parameters at 1800 MHz
Environment Delay Spread Angle spread Max. Doppler shift Macrocellular: Rural flat 0.5 ms 1 degree 200 Hz Macrocellular: Urban 5 ms 20 degrees 120 Hz Macrocellular: Hilly 20 ms 30 degrees 200 Hz Microcellular: Factory, Mall 0.3 ms 120 degrees 10 Hz Microcellular: Indoors, Office 0.1 ms 360 degrees Hz Multipath fading

15 Typical Delay Profiles
Mobile Radio Propagation Channel Typical Delay Profiles Multipath fading

16 How do systems handle delay spreads?
Mobile Radio Propagation Channel How do systems handle delay spreads? Multipath fading

17 Frequency and Time Dispersion
Mobile Radio Propagation Channel Frequency and Time Dispersion Multipath fading

18 Scatter Function of a Multipath Mobile Channel
Mobile Radio Propagation Channel Scatter Function of a Multipath Mobile Channel Gives power as function of Doppler Shift (derived from angle ) f Excess Delay Example of a scatter plot Horizontal axes: x-axis: Excess delay time y-axis: Doppler shift Vertical axis z-axis: received power Multipath fading

19 Scatter Function of a Multipath Mobile Channel
Mobile Radio Propagation Channel Scatter Function of a Multipath Mobile Channel Example of a scatter plot Excess Delay Doppler Shift derived from angle f Multipath fading

20 Correlation of Fading vs. Frequency Separation
Mobile Radio Propagation Channel Correlation of Fading vs. Frequency Separation Multipath fading

21 Mobile Radio Propagation Channel
Multipath fading

22 Mobile Radio Propagation Channel
Coherence Bandwidth Multipath fading

23 Effects of fading on modulated radio signals

24 Effects of Multipath (I)
Mobile Radio Propagation Channel Effects of Multipath (I) Frequency Time Narrowband Frequency Time Wideband Frequency Time OFDM Multipath reception and user mobility lead to channel behavior that is time and frequency dependent. In the following frequency-time diagrams, we depict where in frequency and when in time most of the bit energy is located. It is important to select a modulation scheme that is appropriate for the Doppler Spread and the Delay Spread of the channel. In narrowband communication (NB), the occupied bandwidth is small and the bit duration is long. The bit energy footprint is stretched in vertical direction. Intersymbol interference is neglectable is the bit duration is, say, ten times or more longer than the delay spread. However, due to multipath the entire signal (bandwidth) may vanish in a deep fade. Is fading is very fast, the channel may change during a bit transmission. This can occur if the Doppler spread is large compared to the transmit bandwidth. In wideband transmission (WB), i.e., transmission at high bit rate, the signal is unlikely to vanish completely in a deep fade, because its bandwidth is so wide that some components will be present at frequencies where the channel is good. Such frequency selective fading, however, leads to intersymbol interference, which must be handled, for instance by an adaptive equalizer. In MultiCarrier or OFDM systems, multiple bits are transmitted in parallel over multiple subcarriers. If one subcarrier is in a fade, the other may not. Error correction coding can be used to correct bit errors on faded subcarriers. Rapid fading (Doppler) may erode the orthogonality of closely spaced subcarriers.

25 Effects of Multipath (II)
Mobile Radio Propagation Channel Effects of Multipath (II) Frequency Time + - DS-CDMA Frequency Time + - Hopping Time Frequency + - MC-CDMA Direct Sequence intentionally broadens the transmit spectrum by multiplying user bits with a fast random sequence. The wideband signal is unlikely to fade completely. If frequency selective fading occurs, the receiver sees a series of time-shifted versions of the chipped bit. A ‘rake’ receiver can separate the individual resolvable paths. Frequency Hopping: The carrier frequency is shifted frequently, to avoid fades or narrowband interference. While the signal may vanish during one hop (at a particular frequency), most likely other hops jump to frequencies where the channel is good. Error correction is applied to correct bits lost at faded frequencies. Slow and fast hopping methods differ in the relative duration spent at one frequency, compared to the user bit duration. Orthogonal MC-CDMA is a spectrum-spreading method which exploits advantages of OFDM and DS-CDMA. Each user bit is transmitted simultaneously (in parallel) over multiple subcarriers. This corresponds to a 90 degree rotation of a bit energy map in the frequency-time plane, when compared to DS-CDMA. While the signal may be lost some subcarriers, reliable communication is ensured through appropriate combining of energy from various subcarriers, taking into account the signal-to-interference ratios. In an interference-free environment, Maximum Ratio Diversity combining is the preferred receive strategy. In a noise free environment, equalization (i.e. making all subcarrier amplitudes equal) is preferred.

26 Time Dispersion Revisited
The duration of fades and the optimum packet length

27 Time Dispersion Revisited: Duration of Fades
Mobile Radio Propagation Channel Time Dispersion Revisited: Duration of Fades Multipath fading

28 Mobile Radio Propagation Channel
Two-State Model Multipath fading

29 Average Fade / Nonfade Duration
Mobile Radio Propagation Channel Average Fade / Nonfade Duration Fade duration

30 Level Crossings per Second
Mobile Radio Propagation Channel Level Crossings per Second Level crossing

31 Average nonfade duration
Mobile Radio Propagation Channel Average nonfade duration Fade duration

32 How to handle long fades when the user is stationary?
Mobile Radio Propagation Channel How to handle long fades when the user is stationary? Fade duration

33 Mobile Radio Propagation Channel
Optimal Packet length Fade duration

34 Mobile Radio Propagation Channel
Optimal Packet length fc = 900 MHz 72 km/h (v=20 m/s) fade margin 10 dB Fade duration

35 Derivation of Optimal Packet length
Mobile Radio Propagation Channel Derivation of Optimal Packet length Fade duration

36 Mobile Radio Propagation Channel
Average fade duration Fade duration

37 Conclusion Time and Frequency Dispersion
The multipath channel is characterized by two effects: Time and Frequency Dispersion Time Dispersion effects are proportional to speed and carrier frequency System designer needs to anticipate for channel anomalies Multipath fading


Download ppt "Statistical Description of Multipath Fading"

Similar presentations


Ads by Google